RATIONALE: Drugs used in chemotherapy work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving more than one drug (combination chemotherapy) and giving chemotherapy after surgery may kill more tumor cells. Monoclonal antibodies, such as trastuzumab, can block cancer growth in different ways. Some block the ability of cancer cells to grow and spread. Others find cancer cells and help kill them or carry cancer-killing substances to them. It is not yet known whether combination chemotherapy is more effective with trastuzumab in treating breast cancer.

PURPOSE: This randomized phase III clinical trial is studying chemotherapy with or without trastuzumab after surgery to see how well they work in treating women with invasive breast cancer.

HER2 status of the primary tumor must be evaluated prior to randomization; all testing performed must indicate that the tumor is HER2-low as defined below:

The IHC staining results must indicate a score of 1+ (ISH testing is not required) or 2+ (FISH or CISH must also be performed and must indicate that the tumor is HER2-low as described below)

If ISH (FISH or CISH) testing is performed, test results must be as follows and IHC must be 1+ or 2+:

If FISH is performed, the ratio of HER2 to CEP17 must be < 2.0 or, if a ratio was not performed, the HER2 gene copy number must be < 4 per nucleus

If CISH is performed, the result must indicate a HER2 gene copy number of < 4 per nucleus

NOTE: If the IHC staining intensity is reported as a range, e.g., 0 to 1+ or 1+ to 2+, the higher intensity score in the range should be used to determine eligibility.

No primary tumor with any of the following HER2 testing results:

IHC staining intensity of 0 or 3+

FISH with a ratio of HER2 to CEP17 ≥ 2.0 or HER2 copy number ≥ 4 per nucleus

CISH result indicating HER2-positive or HER2 gene copy number ≥ 4 per nucleus

The patient must have undergone either a total mastectomy or breast-conserving surgery (lumpectomy) (patients who have had a nipple-sparing mastectomy are eligible)

For patients who undergo lumpectomy, the margins of the resected specimen must be histologically free of invasive tumor and DCIS as determined by the local pathologist; if pathologic examination demonstrates tumor at the line of resection, additional operative procedures may be performed to obtain clear margins; if tumor is still present at the resected margin after re-excision(s), the patient must undergo total mastectomy to be eligible (patients with margins positive for LCIS are eligible without additional resection)

For patients who undergo mastectomy, margins must be free of gross residual tumor (patients with microscopic positive margins are eligible as long as post-mastectomy RT of the chest wall will be administered)

The interval between the last surgery for breast cancer (treatment or staging) and randomization must be no more than 84 days

The patient must have completed one of the procedures for evaluation of pathologic nodal status listed below:

Sentinel lymphadenectomy alone:

If pathologic nodal staging based on sentinel lymphadenectomy is pN0 or pN1b

If pathologic nodal staging based on sentinel lymphadenectomy is pN1mi or pN1a, the primary tumor must be T1 or T2 by pathologic evaluation and the nodal involvement must be limited to 1 or 2 positive nodes

Sentinel lymphadenectomy followed by removal of additional non-sentinel lymph nodes if the sentinel node (SN) is positive

Axillary lymphadenectomy with or without SN isolation procedures

The patient must have ER analysis performed on the primary tumor prior to randomization; if ER analysis is negative, then PgR analysis must also be performed (either the core biopsy or surgical resection specimen can be used for ER/PgR testing); patients with a primary tumor that is hormone receptor-positive or receptor-negative are eligible

PATIENT CHARACTERISTICS:

Pre- or postmenopausal

ECOG performance status of 0 or 1

ANC must be ≥ 1,200/mm^3

Platelet count must be ≥ 100,000/mm^3

Hemoglobin must be ≥ 10 g/dL

Total bilirubin must be ≤ ULN for the lab unless the patient has a bilirubin elevation > ULN to 1.5 x ULN due to Gilbert disease or similar syndrome involving slow conjugation of bilirubin

Alkaline phosphatase must be ≤ 2.5 x ULN for the lab

AST must be ≤ 1.5 x ULN for the lab (if ALT is performed instead of AST [per institution's standard practice], the ALT value must be ≤ 1.5 x ULN; if both were performed, the AST must be ≤ 1.5 x ULN)

Alkaline phosphatase and AST may not both be > the ULN

Patients with AST or alkaline phosphatase > ULN are eligible for inclusion in the study if liver imaging (CT, MRI, PET-CT, or PET scan) performed within 90 days prior to randomization does not demonstrate metastatic disease and the above requirements are met

Patients with alkaline phosphatase that is > ULN but ≤ 2.5 x ULN or unexplained bone pain are eligible for inclusion in the study if a bone scan, PET-CT scan, or PET scan performed within 90 days prior to randomization does not demonstrate metastatic disease

The most recent postoperative serum creatinine performed within 6 weeks prior to randomization must be ≤ ULN for the lab

Not pregnant or nursing

Negative pregnancy test

LVEF assessment must be performed within 90 days prior to randomization; LVEF assessment performed by 2-D echocardiogram is preferred, however, MUGA scan may be substituted based on institutional preferences

For patients who will receive the TC chemotherapy regimen, the LVEF must be ≥ 50% regardless of the cardiac-imaging facility's lower limit of normal

For patients who will receive the AC→WP chemotherapy regimen, the LVEF must be ≥ 55% regardless of the cardiac-imaging facility's lower limit of normal

NOTE: Since the pre-entry LVEF serves as the baseline for comparing subsequent LVEF assessments, it is critical that this baseline study be an accurate assessment. If the baseline LVEF is > 70%, the investigator is encouraged to have the accuracy of the initial LVEF result confirmed and repeat the test if the accuracy is uncertain.

No history of non-breast malignancies (except for in situ cancers treated only by local excision and basal cell and squamous cell carcinomas of the skin) within 5 years prior to randomization

No cardiac disease (history of and/or active disease) that would preclude the use of the drugs included in the treatment regimens, including, but not limited to:

Active cardiac disease:

Angina pectoris that requires the current use of anti-anginal medication